The three points move Liverpool into third place, just a point behind Manchester United and four behind Manchester City who have a game in hand. They face Brighton next as they look to make it three wins in a row. West Ham remain fifth but are likely to be leapfrogged by Tottenham who sit two points behind with two games in hand.
Moyes will be hoping his side can get back to winning ways when they take on Aston Villa midweek.
Three brilliant second-half goals from the Premier League champions means they leave the London Stadium with a 3-1 victory over West Ham. After a fairly uneventful opening 45 minutes, Salah broke the deadlock in the 57th minute when he curled an effort into the far corner. And the Egyptian doubled Liverpool's lead not long after with another spectacularly taken goal at the end of a lightning counter-attack.
Wijnaldum made it three in the 84th minute before Dawson's consolation goal took some of the gloss off the performance.